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Options c and d are meant to be 2 and 4 respectively The intensity of light is inversely proportional to the square of its distance from the source (i.e. Intensity ∝ 1 / d^2 ). So if 1/d^2 = 1 unit then 1 / (d/2)^2 = 4 (use mathematics here)

Well, we set aside one bead as a reference point to DISTINGUISH the start/ends of the circle However if all beads are identical, then pulling aside one does not do anything as a reference point and thus the 'method' breaks down. It is then clear that there is only 1 possible arrangement for the...

^ I'm glad you are aware of things like that (statements without logical reinforcement) So: We set aside one bead (either black or white, doesn't matter) to serve as a reference point. Then there are 7! arrangements for the remaining beads. However there STILL exists on the circle 3 black and 5...

For a: Why did you introduce a second point P(2ap,ap^2)? I thought you would just focus on what you're given; point Q(2aq,aq^2) and point S(0,a). And two points is sufficient to find an equation

a: The focal chord is the chord that passes through the focus S(0,a) in this case So you can find the gradient m of QS using y-y1/x-x1 (rise/run) Then apply the formula y-y1 = m(x-x1) to find the equation of the chord b: The latus rectum is the focal chord parallel to the directrix. In this...

a. Use y-y1 = m(x-x1) b. Use the fact that a point P(x,y) on a parabola is equidistant from the focus and directrix.

What is significant about 79.9? o_O

Well the watt is a measurement of joules per second, so from there you should be able to answer the questions. Also, the kilowatt-hour is just a unit of energy consumption used for convenience and manageability (as you will see in the first example) Here's the first one: ai. 2000J/s x (6 x 60 x...

Hint: Pythagoras of Samos

You seem eager to perform but take year 11 easy and do not stress too much; burnout. As for studying rituals and organisation, experiment! I predict after this comment will follow a vast array of tips, sometimes in contradiction to other members' inputs. If anything, extract from this that...

What is mathematics extension 3 lol? :P

That's okay :) When in doubt, go back to your foundations and use the tools you've learnt in mathematics.

Trust your gut instinct. If you want to excel in higher level math, you have to develop insight - and that is only achievable through experience and fault. As for base, it can be anything in a triangle, depending on perspective. The only question here is which is most efficient for the algebra.

Ah, finally worked it out; ending was a little tricky. Start with what you know about triangles: How do you find the area of one? Which method seems most suitable to your question? Then go for it.

Haha nice knock knock joke!

You don't know how best you learn despite ~11 years in academic institutions? :S

Graph y = sin x You will see that it is periodic like a transverse wave in physics with "amplitude" 1 (i.e. range: -1 <= y <= 1 ) So when you have y = 2sin x (which is the form of the question), you will have twice the amplitude (i.e. range: -2 <= y <= 2) So by equating 2sin(x+120) = +- 2, you...

As in, what is your equation to say "RHS"? There is no "given" equation - just an expression. But yeah 2sin(x+120) = +-2 is what you meant

I believe appreciation is just as strong a factor. Perhaps passion is derived from appreciation. I originally hated mathematics; it was repetitive, and arduous (at the time). And then I met someone who lead me to realise my own ignorance, and how prideful I was. I began to appreciate the...

You're accelerated? Consider taking higher levels of mathematics if you find general too easy. On topic: I don't really care much for year 11. I'm polishing year 12 whilst everyone is studying for their yearlies. They will beat me but I don't mind because my foundations are there and I don't...